A New Timing Signature of Black Hole Spin: Time-Delay Asymmetry in Kerr Accretion Flows

TL;DR

This paper presents a novel general-relativistic timing observable that detects black hole spin by measuring asymmetries in photon arrival times caused by Kerr spacetime effects, offering a new method for probing black hole rotation.

Contribution

The authors introduce a new timing asymmetry measure based on photon time delays in Kerr spacetime, validated in the Schwarzschild limit, and applicable for detecting black hole spin.

Findings

Timing asymmetry $A_t$ increases with black hole spin.

Maximum asymmetry occurs near the black hole and at high observer inclinations.

Physical timing offsets can reach seconds to hours in supermassive black hole systems.

Abstract

We introduce a new general-relativistic timing observable that measures the breaking of reflection symmetry in photon arrival times caused by black hole spin. Using backward ray tracing in the Kerr spacetime, we construct time-delay maps across the observer image plane and define a mirror-paired asymmetry based on photons arriving from opposite sides of the projected spin axis. In the Schwarzschild limit ($a=0$), the asymmetry vanishes to numerical precision, providing a stringent validation test of the method. For rotating black holes, Kerr rotation breaks the left-right propagation symmetry of null geodesics, producing systematic differences between prograde and retrograde photon trajectories and resulting in a nonzero mirror-paired timing asymmetry, $A_t$. We find that $A_t$ increases with spin and depends strongly on observer inclination and emission radius, with the largest signals arising from emission close to the black hole and from intermediate to high inclinations. Converting the dimensionless asymmetry into physical units yields timing offsets ranging from seconds to hours for representative supermassive black hole systems. Unlike traditional timing analyses based on spatially integrated signals, the observable introduced here isolates directional information encoded in Kerr photon propagation and provides a physically motivated timing signature of black hole rotation. We discuss the implications of this effect for strong-gravity timing studies and X-ray reverberation mapping.